Finding a suitable chinese input on your operating system can be a pain. I have been trying several operating systems and tried various forms of chinese inputs. Below are the best recommended tools for chinese input. Firstly, there are 2 things you should know. There are 2 main types of chinese characters still used in many parts of the world.

They are Traditional Chinese and Simplified Chinese respectively. Both are currently in use with equal popularity. Traditional chinese is the more complex form of writing that involves more stokes. The simplified chinese is the equavalent with less strokes. Traditional Chinese is popularly used in Hong Kong, Taiwan and as KanJi in Japan. Simplified Chinese is used in China, Singapore and Malaysia.

If you are learning Chinese mandarin, I would advise to stick to the simplified chinese. Most of the text is similar and once you master simplified chinese, picking up traditional chinese would be easier than 123. For simplified chinese, the most popular way of chinese entry is using pinyin, meaning construction of word by Sound. This pinyin uses english alphabets and sounds to construct chinese words. Many people learning chinese often use pinyin but there has not been enough emphasis on the tones. Its like accents in european languages. There are 4 major tones (only 4 , no more and no less) in chinese pin yin.

MacOS X

Mac IME
Default Chinese input for Mac

Fun Input Toy
http://fit.coollittlethings.com/

SunPinYin
http://code.google.com/p/sunpinyin/

Windows

Google Pinyin
http://www.google.com/ime/pinyin/

Linux Ubuntu

Installing chinese on ubuntu linux is quite straight forward. I find that the detail input for chinese is fairly good enough.

goto System -> Administration -> Language Support
Check chinese in the list and also check enable support to input complex characters.
reboot. The system and you are there.